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  <h1>Source code for scitools.MovingPlotWindow</h1><div class="highlight"><pre>
<span class="sd">&quot;&quot;&quot;Manage a moving plot window for displaying very long time series.&quot;&quot;&quot;</span>
<span class="kn">import</span> <span class="nn">time</span>

<div class="viewcode-block" id="MovingPlotWindow"><a class="viewcode-back" href="../../MovingPlotWindow.html#scitools.MovingPlotWindow.MovingPlotWindow">[docs]</a><span class="k">class</span> <span class="nc">MovingPlotWindow</span><span class="p">:</span>
    <span class="sd">&#39;&#39;&#39;</span>
<span class="sd">    Make a plot window that follows the tip (end) of a very long</span>
<span class="sd">    time series.</span>

<span class="sd">    Example::</span>

<span class="sd">        def demo(I, k, dt, T, mode=&#39;continuous movement&#39;):</span>
<span class="sd">            &quot;&quot;&quot;</span>
<span class="sd">            Solve u&#39; = -k**2*u, u(0)=I, u&#39;(0)=0 by a finite difference</span>
<span class="sd">            method with time steps dt, from t=0 to t=T.</span>
<span class="sd">            &quot;&quot;&quot;</span>
<span class="sd">            if dt &gt; 2./k:</span>
<span class="sd">                print &#39;Unstable scheme&#39;</span>
<span class="sd">            N = int(round(T/float(dt)))</span>
<span class="sd">            u = zeros(N+1)</span>
<span class="sd">            t = linspace(0, T, N+1)</span>

<span class="sd">            umin = -1.2*I</span>
<span class="sd">            umax = -umin</span>
<span class="sd">            period = 2*pi/k  # period of the oscillations</span>
<span class="sd">            window_width =</span>
<span class="sd">            plot_manager = MovingPlotWindow(</span>
<span class="sd">                             window_width, dt, yaxis=[umin, umax],</span>
<span class="sd">                             mode=mode)</span>
<span class="sd">            u[0] = I</span>
<span class="sd">            u[1] = u[0] - 0.5*dt**2*k**2*u[0]</span>
<span class="sd">            for n in range(1,N):</span>
<span class="sd">                u[n+1] = 2*u[n] - u[n-1] - dt**2*k**2*u[n]</span>

<span class="sd">                if plot_manager.plot(n):</span>
<span class="sd">                    s = plot_manager.first_index_in_plot</span>
<span class="sd">                    plot(t[s:n+2], u[s:n+2], &#39;r-&#39;,</span>
<span class="sd">                         t[s:n+2], I*cos(k*t)[s:n+2], &#39;b-&#39;,</span>
<span class="sd">                         axis=plot_manager.axis(),</span>
<span class="sd">                         title=&quot;Solution of u&#39;&#39; + k^2 u = 0 for t=%6.3f (mode: %s)&quot; % (t[n+1], mode))</span>
<span class="sd">                plot_manager.update(n)</span>
<span class="sd">    &#39;&#39;&#39;</span>

<div class="viewcode-block" id="MovingPlotWindow.__init__"><a class="viewcode-back" href="../../MovingPlotWindow.html#scitools.MovingPlotWindow.MovingPlotWindow.__init__">[docs]</a>    <span class="k">def</span> <span class="nf">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">window_width</span><span class="p">,</span> <span class="n">dt</span><span class="p">,</span> <span class="n">yaxis</span><span class="o">=</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span><span class="mi">1</span><span class="p">],</span>
                 <span class="n">mode</span><span class="o">=</span><span class="s">&#39;continuous movement&#39;</span><span class="p">,</span>
                 <span class="n">pause</span><span class="o">=</span><span class="mf">1.5</span><span class="p">):</span>
        <span class="sd">&quot;&quot;&quot;</span>
<span class="sd">        ====================  ====================================</span>
<span class="sd">        Argument              Description</span>
<span class="sd">        ====================  ====================================</span>
<span class="sd">        window_width          tmax-tmin in a plot window</span>
<span class="sd">        dt                    time step (constant)</span>
<span class="sd">        yaxis                 extent of y axis</span>
<span class="sd">        mode                  method for moving the plot window,</span>
<span class="sd">                              see below.</span>
<span class="sd">        ====================  ====================================</span>

<span class="sd">        The mode parameter has three values:</span>

<span class="sd">          * ``&#39;continuous movement&#39;``:</span>
<span class="sd">            the plot window moves one time step for each plot.</span>
<span class="sd">          * ``&#39;continuous drawing&#39;``: the curves are drawn from left</span>
<span class="sd">            to right, one step at a time, and plot window jumps</span>
<span class="sd">            when the curve reaches the end.</span>
<span class="sd">          * ``&#39;jumps&#39;``: the curves are shown in a window for a time</span>
<span class="sd">            equal to the pause argument, then the axis jumps</span>
<span class="sd">            to a new time window of the same length</span>


<span class="sd">        See also the test block of the module for</span>
<span class="sd">        testing out the three different modes of this class.</span>
<span class="sd">        &quot;&quot;&quot;</span>
        <span class="bp">self</span><span class="o">.</span><span class="n">taxis_length_in_steps</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="nb">round</span><span class="p">(</span><span class="n">window_width</span><span class="o">/</span><span class="nb">float</span><span class="p">(</span><span class="n">dt</span><span class="p">)))</span>
        <span class="bp">self</span><span class="o">.</span><span class="n">dt</span> <span class="o">=</span> <span class="n">dt</span>
        <span class="bp">self</span><span class="o">.</span><span class="n">mode</span> <span class="o">=</span> <span class="n">mode</span>
        <span class="bp">self</span><span class="o">.</span><span class="n">taxis_length</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">taxis_length_in_steps</span><span class="o">*</span><span class="bp">self</span><span class="o">.</span><span class="n">dt</span>
        <span class="bp">self</span><span class="o">.</span><span class="n">first_index_in_plot</span> <span class="o">=</span> <span class="mi">0</span>
        <span class="bp">self</span><span class="o">.</span><span class="n">taxis_min</span> <span class="o">=</span> <span class="mi">0</span>
        <span class="bp">self</span><span class="o">.</span><span class="n">yaxis</span> <span class="o">=</span> <span class="n">yaxis</span>
        <span class="bp">self</span><span class="o">.</span><span class="n">pause</span> <span class="o">=</span> <span class="n">pause</span>
        <span class="bp">self</span><span class="o">.</span><span class="n">n_prev</span> <span class="o">=</span> <span class="mi">0</span>
</div>
<div class="viewcode-block" id="MovingPlotWindow.axis"><a class="viewcode-back" href="../../MovingPlotWindow.html#scitools.MovingPlotWindow.MovingPlotWindow.axis">[docs]</a>    <span class="k">def</span> <span class="nf">axis</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
        <span class="sd">&quot;&quot;&quot;Return the axis limits as a list ``[xmin, xmax, ymin, ymax]``.&quot;&quot;&quot;</span>
        <span class="k">return</span> <span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">taxis_min</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">taxis_min</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">taxis_length</span><span class="p">,</span>
                <span class="bp">self</span><span class="o">.</span><span class="n">yaxis</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="bp">self</span><span class="o">.</span><span class="n">yaxis</span><span class="p">[</span><span class="mi">1</span><span class="p">]]</span>
</div>
<div class="viewcode-block" id="MovingPlotWindow.plot"><a class="viewcode-back" href="../../MovingPlotWindow.html#scitools.MovingPlotWindow.MovingPlotWindow.plot">[docs]</a>    <span class="k">def</span> <span class="nf">plot</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">n</span><span class="p">):</span>
        <span class="sd">&quot;&quot;&quot;</span>
<span class="sd">        Return True if a plot is to be drawn at time step number ``n``,</span>
<span class="sd">        otherwise return False.</span>
<span class="sd">        &quot;&quot;&quot;</span>
        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">mode</span> <span class="o">==</span> <span class="s">&#39;continuous movement&#39;</span><span class="p">:</span>
            <span class="k">return</span> <span class="bp">True</span>

        <span class="k">elif</span> <span class="bp">self</span><span class="o">.</span><span class="n">mode</span> <span class="o">==</span> <span class="s">&#39;continuous drawing&#39;</span><span class="p">:</span>
            <span class="c"># Update self.first_index_in_plot and self.taxis_min</span>
            <span class="c"># every self.taxis_length_in_steps time step</span>
            <span class="k">if</span> <span class="n">n</span> <span class="o">%</span> <span class="bp">self</span><span class="o">.</span><span class="n">taxis_length_in_steps</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
                <span class="bp">self</span><span class="o">.</span><span class="n">taxis_min</span> <span class="o">+=</span> <span class="bp">self</span><span class="o">.</span><span class="n">taxis_length</span>
                <span class="bp">self</span><span class="o">.</span><span class="n">first_index_in_plot</span> <span class="o">+=</span> <span class="bp">self</span><span class="o">.</span><span class="n">taxis_length_in_steps</span>
            <span class="c"># Always plot the curves in continuous drawing</span>
            <span class="k">return</span> <span class="bp">True</span>
        <span class="k">else</span><span class="p">:</span>
            <span class="c"># Plot every self.taxis_length_in_steps time step only</span>
            <span class="k">if</span> <span class="p">(</span><span class="n">n</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span> <span class="o">%</span> <span class="bp">self</span><span class="o">.</span><span class="n">taxis_length_in_steps</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
                <span class="k">return</span> <span class="bp">True</span>
            <span class="k">else</span><span class="p">:</span>
                <span class="k">return</span> <span class="bp">False</span>
</div>
<div class="viewcode-block" id="MovingPlotWindow.update"><a class="viewcode-back" href="../../MovingPlotWindow.html#scitools.MovingPlotWindow.MovingPlotWindow.update">[docs]</a>    <span class="k">def</span> <span class="nf">update</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">n</span><span class="p">):</span>
        <span class="sd">&quot;&quot;&quot;Update the plot manager (``MovingPlotWindow``) at time step ``n``.&quot;&quot;&quot;</span>
        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">mode</span> <span class="o">==</span> <span class="s">&#39;continuous movement&#39;</span><span class="p">:</span>
            <span class="k">if</span> <span class="n">n</span> <span class="o">&gt;</span> <span class="bp">self</span><span class="o">.</span><span class="n">taxis_length_in_steps</span><span class="p">:</span>
                <span class="bp">self</span><span class="o">.</span><span class="n">taxis_min</span> <span class="o">+=</span> <span class="bp">self</span><span class="o">.</span><span class="n">dt</span>
                <span class="bp">self</span><span class="o">.</span><span class="n">first_index_in_plot</span> <span class="o">+=</span> <span class="n">n</span> <span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">n_prev</span>
            <span class="bp">self</span><span class="o">.</span><span class="n">n_prev</span> <span class="o">=</span> <span class="n">n</span>

        <span class="k">elif</span> <span class="bp">self</span><span class="o">.</span><span class="n">mode</span> <span class="o">==</span> <span class="s">&#39;jumps&#39;</span> <span class="ow">and</span> \
               <span class="p">(</span><span class="n">n</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span> <span class="o">%</span> <span class="bp">self</span><span class="o">.</span><span class="n">taxis_length_in_steps</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
            <span class="c"># After plot is shown, sleep and then update plot</span>
            <span class="c"># window parameters</span>
            <span class="n">time</span><span class="o">.</span><span class="n">sleep</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">pause</span><span class="p">)</span>
            <span class="bp">self</span><span class="o">.</span><span class="n">taxis_min</span> <span class="o">+=</span> <span class="bp">self</span><span class="o">.</span><span class="n">taxis_length</span>
            <span class="bp">self</span><span class="o">.</span><span class="n">first_index_in_plot</span> <span class="o">+=</span> <span class="bp">self</span><span class="o">.</span><span class="n">taxis_length_in_steps</span>
</div></div>
<span class="k">def</span> <span class="nf">_demo</span><span class="p">(</span><span class="n">I</span><span class="p">,</span> <span class="n">k</span><span class="p">,</span> <span class="n">dt</span><span class="p">,</span> <span class="n">T</span><span class="p">,</span> <span class="n">mode</span><span class="o">=</span><span class="s">&#39;continuous movement&#39;</span><span class="p">):</span>
    <span class="sd">&quot;&quot;&quot;</span>
<span class="sd">    Solve u&#39; = -k**2*u, u(0)=I, u&#39;(0)=0 by a finite difference</span>
<span class="sd">    method with time steps dt, from t=0 to t=T.</span>
<span class="sd">    &quot;&quot;&quot;</span>
    <span class="k">if</span> <span class="n">dt</span> <span class="o">&gt;</span> <span class="mf">2.</span><span class="o">/</span><span class="n">k</span><span class="p">:</span>
        <span class="k">print</span> <span class="s">&#39;Unstable scheme&#39;</span>
    <span class="n">N</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="nb">round</span><span class="p">(</span><span class="n">T</span><span class="o">/</span><span class="nb">float</span><span class="p">(</span><span class="n">dt</span><span class="p">)))</span>
    <span class="n">u</span> <span class="o">=</span> <span class="n">zeros</span><span class="p">(</span><span class="n">N</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span>
    <span class="n">t</span> <span class="o">=</span> <span class="n">linspace</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">T</span><span class="p">,</span> <span class="n">N</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span>

    <span class="n">umin</span> <span class="o">=</span> <span class="o">-</span><span class="mf">1.2</span><span class="o">*</span><span class="n">I</span>
    <span class="n">umax</span> <span class="o">=</span> <span class="o">-</span><span class="n">umin</span>
    <span class="n">period</span> <span class="o">=</span> <span class="mi">2</span><span class="o">*</span><span class="n">pi</span><span class="o">/</span><span class="n">k</span>  <span class="c"># period of the oscillations</span>
    <span class="n">plot_manager</span> <span class="o">=</span> <span class="n">MovingPlotWindow</span><span class="p">(</span><span class="mi">8</span><span class="o">*</span><span class="n">period</span><span class="p">,</span> <span class="n">dt</span><span class="p">,</span> <span class="n">yaxis</span><span class="o">=</span><span class="p">[</span><span class="n">umin</span><span class="p">,</span> <span class="n">umax</span><span class="p">],</span>
                                    <span class="n">mode</span><span class="o">=</span><span class="n">mode</span><span class="p">)</span>
    <span class="n">u</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="n">I</span>
    <span class="n">u</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="n">u</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">-</span> <span class="mf">0.5</span><span class="o">*</span><span class="n">dt</span><span class="o">**</span><span class="mi">2</span><span class="o">*</span><span class="n">k</span><span class="o">**</span><span class="mi">2</span><span class="o">*</span><span class="n">u</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
    <span class="k">for</span> <span class="n">n</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="n">N</span><span class="p">):</span>
        <span class="n">u</span><span class="p">[</span><span class="n">n</span><span class="o">+</span><span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="mi">2</span><span class="o">*</span><span class="n">u</span><span class="p">[</span><span class="n">n</span><span class="p">]</span> <span class="o">-</span> <span class="n">u</span><span class="p">[</span><span class="n">n</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="o">-</span> <span class="n">dt</span><span class="o">**</span><span class="mi">2</span><span class="o">*</span><span class="n">k</span><span class="o">**</span><span class="mi">2</span><span class="o">*</span><span class="n">u</span><span class="p">[</span><span class="n">n</span><span class="p">]</span>

        <span class="k">if</span> <span class="n">plot_manager</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
            <span class="n">s</span> <span class="o">=</span> <span class="n">plot_manager</span><span class="o">.</span><span class="n">first_index_in_plot</span>
            <span class="n">plot</span><span class="p">(</span><span class="n">t</span><span class="p">[</span><span class="n">s</span><span class="p">:</span><span class="n">n</span><span class="o">+</span><span class="mi">2</span><span class="p">],</span> <span class="n">u</span><span class="p">[</span><span class="n">s</span><span class="p">:</span><span class="n">n</span><span class="o">+</span><span class="mi">2</span><span class="p">],</span> <span class="s">&#39;r-&#39;</span><span class="p">,</span>
                 <span class="n">t</span><span class="p">[</span><span class="n">s</span><span class="p">:</span><span class="n">n</span><span class="o">+</span><span class="mi">2</span><span class="p">],</span> <span class="n">I</span><span class="o">*</span><span class="n">cos</span><span class="p">(</span><span class="n">k</span><span class="o">*</span><span class="n">t</span><span class="p">)[</span><span class="n">s</span><span class="p">:</span><span class="n">n</span><span class="o">+</span><span class="mi">2</span><span class="p">],</span> <span class="s">&#39;b-&#39;</span><span class="p">,</span>
                 <span class="n">axis</span><span class="o">=</span><span class="n">plot_manager</span><span class="o">.</span><span class="n">axis</span><span class="p">(),</span>
                 <span class="n">title</span><span class="o">=</span><span class="s">&quot;Solution of u&#39;&#39; + k^2 u = 0 for t=</span><span class="si">%6.3f</span><span class="s"> (mode: </span><span class="si">%s</span><span class="s">)&quot;</span> \
                 <span class="o">%</span> <span class="p">(</span><span class="n">t</span><span class="p">[</span><span class="n">n</span><span class="o">+</span><span class="mi">1</span><span class="p">],</span> <span class="n">mode</span><span class="p">))</span>
        <span class="n">plot_manager</span><span class="o">.</span><span class="n">update</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>

<span class="k">if</span> <span class="n">__name__</span> <span class="o">==</span> <span class="s">&#39;__main__&#39;</span><span class="p">:</span>
    <span class="kn">from</span> <span class="nn">scitools.std</span> <span class="kn">import</span> <span class="o">*</span>
    <span class="n">T</span> <span class="o">=</span> <span class="mi">40</span>
    <span class="n">_demo</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">pi</span><span class="p">,</span> <span class="mf">0.1</span><span class="p">,</span> <span class="n">T</span><span class="p">,</span> <span class="n">mode</span><span class="o">=</span><span class="s">&#39;continuous movement&#39;</span><span class="p">)</span>
    <span class="n">time</span><span class="o">.</span><span class="n">sleep</span><span class="p">(</span><span class="mi">10</span><span class="p">)</span>
    <span class="n">figure</span><span class="p">()</span>
    <span class="n">_demo</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">pi</span><span class="p">,</span> <span class="mf">0.1</span><span class="p">,</span> <span class="n">T</span><span class="p">,</span> <span class="n">mode</span><span class="o">=</span><span class="s">&#39;continuous drawing&#39;</span><span class="p">)</span>
    <span class="n">time</span><span class="o">.</span><span class="n">sleep</span><span class="p">(</span><span class="mi">10</span><span class="p">)</span>
    <span class="n">figure</span><span class="p">()</span>
    <span class="n">_demo</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">pi</span><span class="p">,</span> <span class="mf">0.1</span><span class="p">,</span> <span class="n">T</span><span class="p">,</span> <span class="n">mode</span><span class="o">=</span><span class="s">&#39;jumps&#39;</span><span class="p">)</span>
    <span class="n">time</span><span class="o">.</span><span class="n">sleep</span><span class="p">(</span><span class="mi">10</span><span class="p">)</span>
</pre></div>

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